Space of modular forms of level 9, weight 9, and Character 9.b

• Label: 9.9.b
• Level: $9$
• Weight: $9$
• Character orbit: 9.b
• Rep. character: $\chi_{9}(8,\cdot)$
• Character field: $\Q$
• Dimension: $2$
• Newform subspaces: $1$
• Sturm bound: $9$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 9 = 3^{2} \)
Weight:	\( k \)	\(=\)	\( 9 \)
Character orbit:	\([\chi]\)	\(=\)	9.b (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 3 \)
Character field:			\(\Q\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(9\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{9}(9, [\chi])\).

	Total	New	Old
Modular forms	10	2	8
Cusp forms	6	2	4
Eisenstein series	4	0	4

Trace form

2 * q + 476 * q^4 + 3304 * q^7 - 8388 * q^10 - 52544 * q^13 + 104072 * q^16 + 93280 * q^19 + 181296 * q^22 - 1173154 * q^25 + 786352 * q^28 - 392888 * q^31 - 128844 * q^34 + 5638828 * q^37 - 4143672 * q^40 - 4426928 * q^43 + 2783952 * q^46 - 6071394 * q^49 - 12505472 * q^52 + 42241968 * q^55 + 5218308 * q^58 - 34810604 * q^61 + 20216432 * q^64 - 28645328 * q^67 - 13856976 * q^70 - 17813984 * q^73 + 22200640 * q^76 + 65517688 * q^79 + 5994252 * q^82 - 30020652 * q^85 + 89560224 * q^88 - 86802688 * q^91 - 13856112 * q^94 - 48903488 * q^97

Decomposition of \(S_{9}^{\mathrm{new}}(9, [\chi])\) into newform subspaces

Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	CM	Self-dual	Twist minimal	Largest	Maximal	Minimal twist	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
9.9.b.a	$9$	$9$	9.b	3.b	$2$	$2$	$2$	$3.666$	\(\Q(\sqrt{-2}) \)	None		✓	✓	✓	9.9.b.a	$2$	$0$	\(0\)	\(0\)	\(0\)	\(3304\)	$3$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta q^{2}+238q^{4}+233\beta q^{5}+1652q^{7}+\cdots\)

Decomposition of \(S_{9}^{\mathrm{old}}(9, [\chi])\) into lower level spaces

\( S_{9}^{\mathrm{old}}(9, [\chi]) \simeq \) \(S_{9}^{\mathrm{new}}(3, [\chi])\)\(^{\oplus 2}\)